1. mean and standard deviation

I have scanned over and over a similar problem on the forum, i just cannot understand.
I understand that i am to read the normal Z tables like a stem plot but cannot find any connection to the answers given.

Plastic buckets are made by machine on a production line. The weight of each bucket is normally distributed with mean 1250g and standard deviation 120g. Let X be the weight of a bucket in a randomly chosen batch.
Mean- 1250 Std. dev = 120

(a) Find Pr(X > 1250) This is the mean so prob has to equal half... (0.5)

(b) Find Pr(1250 < X < 1380)
= Find Z first z = 1380 – 1250 / 120 = 130/120 = 1.083
Pr(1250 < X < 1380) = look up z in tables

(c) Find Pr(1135 < X < 1275)
= Find Z (you need 2 values – lower should work out as -0.958 and upper as 0.208)tutor notes
= Pr(1135 < X < 1275) = look up Z values in tables and add together
It is spelled out for me, i cant see where to go. how to get the Z,

2. Hello,

Originally Posted by roxy
I have scanned over and over a similar problem on the forum, i just cannot understand.
I understand that i am to read the normal Z tables like a stem plot but cannot find any connection to the answers given.

Plastic buckets are made by machine on a production line. The weight of each bucket is normally distributed with mean 1250g and standard deviation 120g. Let X be the weight of a bucket in a randomly chosen batch.
Mean- 1250 Std. dev = 120

(a) Find Pr(X > 1250) This is the mean so prob has to equal half... (0.5)

(b) Find Pr(1250 < X < 1380)
= Find Z first z = 1380 – 1250 / 120 = 130/120 = 1.083
Pr(1250 < X < 1380) = look up z in tables

(c) Find Pr(1135 < X < 1275)
= Find Z (you need 2 values – lower should work out as -0.958 and upper as 0.208)tutor notes
= Pr(1135 < X < 1275) = look up Z values in tables and add together
It is spelled out for me, i cant see where to go. how to get the Z,
The z-table is made up for a standard normal distribution..

So for a random variable X that has a normal distribution, a mean of $\mu$ and a standard dev of $\sigma$, there is Z that has a standard normal distribution :

$Z=\frac{X-\mu}{\sigma}$

So transform $P(1250 $=P(0

Same for $P(1135 $-P(-0.9583 $=P(Z<0.2083)-(1-P(Z<-0.9583))=P(Z<0.2083)+P(Z<-0.9583)-1$

3. Plastic buckets are made by machine on a production line. The weight of each bucket is normally distributed with mean 1250g and standard deviation
(c) Find Pr(1135 < X < 1275)
= Find Z (you need 2 values – lower should work out as -0.958 and upper as 0.208)tutor notes
= Pr(1135 < X < 1275) = look up Z values in tables and add together
It is spelled out for me, i cant see where to go. how to get the Z,[/quote]

For this one fins the two z-score, then look them up to see what probability corresponds.

$z=\frac{x-{\mu}}{\sigma}$

$-.958=\frac{1135-1250}{120}$

Look up in the table and we get .169

$.208=\frac{1275-1250}{120}$

Look up in the table and we get .582

Subtract and we get a probability of .413

4. Thankyou, i will have a look at all the info you sent. sorry i cant give you chocolates, maybe virtual.

5. still stuck

Look up in the table and we get .169

Look up in the table and we get .582

Subtract and we get a probability of .413 _

this .169 and .582 is where i am having trouble. when i look the .958 up in the z tables all i get is .3309 . when i look up z= .208 i find .824